Explanation:
The given sides of the triangle is given below as
[tex]\begin{gathered} a=5 \\ b=8 \\ c=11 \end{gathered}[/tex]
The heron's formula is given below as
[tex]\begin{gathered} A=\sqrt{s(s-a)(s-b)(s-c)} \\ where, \\ s=\frac{a+b+c}{2} \end{gathered}[/tex]
By substituting the values, we will have
[tex]\begin{gathered} s=\frac{a+b+c}{2} \\ s=\frac{5+8+11}{2} \\ s=\frac{24}{2} \\ s=12 \end{gathered}[/tex]
Hence,
The area of the triangle will be
[tex]\begin{gathered} A=\sqrt{s(s-a)(s-b)(s-c)} \\ A=\sqrt{12(12-5)(12-8)(12-11)} \\ A=\sqrt{12(7\times4\times1)} \\ A=\sqrt{336} \\ A=18.33 \end{gathered}[/tex]
Hence,
The final answer is
[tex]\Rightarrow18.33[/tex]
